The highest barrier that a projectile can clear is 11.5 m, when the projectile is launched at an angle of 15.4° above the horizontal. What is the projectile's launch speed?
To find the projectile's launch speed, we can use the kinematic equations of motion. In this case, we'll specifically use the equation for the maximum height reached by a projectile.
The maximum height, h, can be determined using the following equation:
h = (v₀² * sin²(θ)) / (2 * g)
Where:
- h is the maximum height reached by the projectile (11.5 m in this case)
- v₀ is the initial velocity or launch speed of the projectile (what we want to find)
- θ is the launch angle, given as 15.4°
- g is the acceleration due to gravity, which is approximately 9.8 m/s²
Now we'll rearrange the equation to solve for v₀:
v₀ = √((h * 2 * g) / sin²(θ))
Substituting the known values into the equation:
v₀ = √((11.5 * 2 * 9.8) / sin²(15.4°))
Using a scientific calculator or math software, we can evaluate this expression to find the answer:
v₀ ≈ √((11.5 * 2 * 9.8) / sin²(15.4°)) ≈ 18.9 m/s
Therefore, the projectile's launch speed is approximately 18.9 m/s.